Generally, electrical actuators are controlled using signals generated by position sensors. For controlling permanent magnets of electric motors, low resolution sensors, such as Hall sensors, are commonly used for containing costs. These devices, positioned on the stator, sense the rotor magnetic field and generate a voltage signal proportional to the intensity of the magnetic field, as depicted in FIG. 1.
The intensity of the magnetic field decreases when the distance of magnetic poles from the Hall sensor, indicated in FIG. 1 by an arrow, increases, and, thus, the voltage generated by the sensor decreases. The period of the voltage signal generated by the Hall sensor for a mechanical revolution of the rotor depends on the number of polar pairs of the motor. Thus the mechanical resolution of the single sensor increases when the number of polar pairs of the motor itself increases, but the resolution in electrical degrees remains unchanged.
The signal generated by the Hall sensor is analog. Nevertheless, if this signal drives an hysteretic threshold detector, for example, a Schmitt's trigger, the output signal is an ON/OFF type, that is a digital signal is obtained in which information about the position of the rotor is given by leading and trailing edges.
Generally, an electric motor is equipped with three Hall sensors spaced at a distance of 120° one from the other. FIG. 2, for example, depicts a sample sequence of the switching edges generated by the three Hall sensors installed on a Pittman motor 3441S001-R3, and the respective value of the electrical angle. As shown in the figure, a leading or a trailing edge occurs at every 60 electrical degrees.
By way of example, hereinafter reference will be made to this resolution, even if in general it is insufficient for actuating complex control strategies to improve performances of the control system both in terms of ripple of the motor torque, or in terms of Total Harmonic Distortion (or more briefly THD) of the phase currents of the motor.
If the angular position of the rotor is known in correspondence of each switching edge, there is the problem of estimating the angular position between two consecutive edges. The classic method for reconstructing the angular position of the rotor contemplates a linear interpolation operation as a function of the time t elapsed from the last edge and the time t0 elapsed from the last edge and the previous edge, considering that t0 is the time required for rotating of 60 electrical degrees. Accordingly, the angle θ in electrical degrees at the instant t is:
                              θ          ⁡                      (            t            )                          =                                            t                              t                0                                      ·            60                    +                      θ            0                                              (        1        )            wherein θ0 is the angle in electrical degrees associated to the last detected switching edge (FIG. 2). This is equivalent to assuming the rotation speed is constant.
The precision of the estimation of the angular speed of the rotor depends on the validity of the hypothesis of constant speed for calculating the current angular position using the time t0 and on the precision of the Hall sensors. Tests carried out on commercial motors using simple algorithms for calculating the angular position, based on the above mentioned hypothesis, demonstrated that the uncertainty of information provided by Hall sensors implies a significant imprecision of the estimated angular position of the rotor, with a consequent increase of the THD of the phase currents of the motor. Imprecision is essentially due to fabrication limitations of the sensors, imprecise mounting of the sensors, and distortion of the rotor magnetic field.
As far as fabrication limitations are concerned, the amplitude of the hysteresis bandwidth of the threshold detector may lead to systematic errors in aligning the edges of the output signals of the sensor with the respective theoretical angle. Moreover, the sensor provides a signal proportional to the intensity of the sole orthogonal component of the magnetic flux with respect to its own surface. Thus positioning errors of the sensor, such as, for example, a lateral shift or rotation with respect to the vertical axis, generate alignment errors of the edges of the output signal of the sensor with the respective theoretical angle. Moreover, in the latter case, alignment errors differ depending on whether a leading or a trailing edge has been detected. Distortions of the rotor magnetic field may be caused by irregularities of the magnetization of the permanent magnets, fabrication eccentricity, and by the so-called armature reaction, that is by the magnetic field due to current flowing through phase windings of the stator. Therefore a system for estimating the angular position of the rotor of a motor that would allow reduction of errors due to the imprecision of the information provided by Hall sensors would be desirable. Such a system could enhance performances of the control system in terms of motor torque ripple and in terms of THD of the phase currents.